diff --git a/Project.toml b/Project.toml
index f625e9027..92fc3e89b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "KernelFunctions"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
-version = "0.10.41"
+version = "0.10.42"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/transform/chaintransform.jl b/src/transform/chaintransform.jl
index bd4627b19..9129fb84b 100644
--- a/src/transform/chaintransform.jl
+++ b/src/transform/chaintransform.jl
@@ -1,5 +1,5 @@
 """
-    ChainTransform(ts::AbstractVector{<:Transform})
+    ChainTransform(transforms)
 
 Transformation that applies a chain of transformations `ts` to the input.
 
@@ -19,7 +19,7 @@ julia> map(t2 ∘ t1, ColVecs(X)) == ColVecs(A * (l .* X))
 true
 ```
 """
-struct ChainTransform{V<:AbstractVector{<:Transform}} <: Transform
+struct ChainTransform{V} <: Transform
     transforms::V
 end
 
@@ -28,23 +28,23 @@ end
 Base.length(t::ChainTransform) = length(t.transforms)
 
 # Constructor to create a chain transform with an array of parameters
-function ChainTransform(v::AbstractVector{<:Type{<:Transform}}, θ::AbstractVector)
+function ChainTransform(v, θ::AbstractVector)
     @assert length(v) == length(θ)
     return ChainTransform(v.(θ))
 end
 
-Base.:∘(t₁::Transform, t₂::Transform) = ChainTransform([t₂, t₁])
-Base.:∘(t::Transform, tc::ChainTransform) = ChainTransform(vcat(tc.transforms, t))
-Base.:∘(tc::ChainTransform, t::Transform) = ChainTransform(vcat(t, tc.transforms))
+Base.:∘(t₁::Transform, t₂::Transform) = ChainTransform((t₂, t₁))
+Base.:∘(t::Transform, tc::ChainTransform) = ChainTransform(tuple(tc.transforms..., t))
+Base.:∘(tc::ChainTransform, t::Transform) = ChainTransform(tuple(t, tc.transforms...))
 
 (t::ChainTransform)(x) = foldl((x, t) -> t(x), t.transforms; init=x)
 
 function _map(t::ChainTransform, x::AbstractVector)
-    return foldl((x, t) -> map(t, x), t.transforms; init=x)
+    return foldl((x, t) -> _map(t, x), t.transforms; init=x)
 end
 
 set!(t::ChainTransform, θ) = set!.(t.transforms, θ)
-duplicate(t::ChainTransform, θ) = ChainTransform(duplicate.(t.transforms, θ))
+duplicate(t::ChainTransform, θ) = ChainTransform(map(duplicate, t.transforms, θ))
 
 Base.show(io::IO, t::ChainTransform) = printshifted(io, t, 0)
 
diff --git a/test/test_utils.jl b/test/test_utils.jl
index b8c349e37..c506d5a69 100644
--- a/test/test_utils.jl
+++ b/test/test_utils.jl
@@ -274,3 +274,81 @@ function test_AD(AD::Symbol, k::MOKernel, dims=(in=3, out=2, obs=3))
         end
     end
 end
+
+function count_allocs(f, args...)
+    stats = @timed f(args...)
+    return Base.gc_alloc_count(stats.gcstats)
+end
+
+"""
+    constant_allocs_heuristic(f, args1::T, args2::T) where {T}
+
+True if number of allocations associated with evaluating `f(args1...)` is equal to those
+required to evaluate `f(args2...)`. Runs `f` beforehand to ensure that compilation-related
+allocations are not included.
+
+Why is this a good test? In lots of situations it will be the case that the total amount of
+memory allocated by a function will vary as the input sizes vary, but the total _number_
+of allocations ought to be constant. A common performance bug is that the number of
+allocations actually does scale with the size of the inputs (e.g. due to a type
+instability), and we would very much like to know if this is happening.
+
+Typically this kind of condition is not a sufficient condition for good performance, but it
+is certainly a necessary condition.
+
+This kind of test is very quick to conduct (just requires running `f` 4 times). It's also
+easier to write than simply checking that the total number of allocations used to execute
+a function is below some arbitrary `f`-dependent threshold.
+"""
+function constant_allocs_heuristic(f, args1::T, args2::T) where {T}
+
+    # Ensure that we're not counting allocations associated with compilation.
+    f(args1...)
+    f(args2...)
+
+    allocs_1 = count_allocs(f, args1...)
+    allocs_2 = count_allocs(f, args2...)
+    return allocs_1 == allocs_2
+end
+
+"""
+    ad_constant_allocs_heuristic(f, args1::T, args2::T; Δ1=nothing, Δ2=nothing) where {T}
+
+Assesses `constant_allocs_heuristic` for `f`, `Zygote.pullback(f, args...)` and its
+pullback for both of `args1` and `args2`.
+
+`Δ1` and `Δ2` are passed to the pullback associated with `Zygote.pullback(f, args1...)`
+and `Zygote.pullback(f, args2...)` respectively. If left as `nothing`, it is assumed that
+the output of the primal is an acceptable cotangent to be passed to the corresponding
+pullback.
+"""
+function ad_constant_allocs_heuristic(
+    f, args1::T, args2::T; Δ1=nothing, Δ2=nothing
+) where {T}
+
+    # Check that primal has constant allocations.
+    primal_heuristic = constant_allocs_heuristic(f, args1, args2)
+
+    # Check that forwards-pass has constant allocations.
+    forwards_heuristic = constant_allocs_heuristic(
+        (args...) -> Zygote.pullback(f, args...), args1, args2
+    )
+
+    # Check that pullback has constant allocations for both arguments. Run twice to remove
+    # compilation-related allocations.
+
+    # First thing
+    out1, pb1 = Zygote.pullback(f, args1...)
+    Δ1_val = Δ1 === nothing ? out1 : Δ1
+    pb1(Δ1_val)
+    allocs_1 = count_allocs(pb1, Δ1_val)
+
+    # Second thing
+    out2, pb2 = Zygote.pullback(f, args2...)
+    Δ2_val = Δ2 === nothing ? out2 : Δ2
+    pb2(Δ2_val)
+    allocs_2 = count_allocs(pb2, Δ2 === nothing ? out2 : Δ2)
+
+    pullback_heuristic = allocs_1 == allocs_2
+    return primal_heuristic, forwards_heuristic, pullback_heuristic
+end
diff --git a/test/transform/chaintransform.jl b/test/transform/chaintransform.jl
index f8b19cffe..3b6856b1f 100644
--- a/test/transform/chaintransform.jl
+++ b/test/transform/chaintransform.jl
@@ -7,11 +7,11 @@
     f(x) = sin.(x)
     tf = FunctionTransform(f)
 
-    t = ChainTransform([tp, tf])
+    t = ChainTransform((tp, tf))
 
     # Check composition constructors.
-    @test (tf ∘ ChainTransform([tp])).transforms == [tp, tf]
-    @test (ChainTransform([tf]) ∘ tp).transforms == [tp, tf]
+    @test (tf ∘ ChainTransform([tp])).transforms == (tp, tf)
+    @test (ChainTransform([tf]) ∘ tp).transforms == (tp, tf)
 
     # Verify correctness.
     x = ColVecs(randn(rng, 2, 3))
@@ -27,5 +27,14 @@
         randn(rng, 4);
         ADs=[:ForwardDiff, :ReverseDiff],  # explicitly pass ADs to exclude :Zygote
     )
-    @test_broken "test_AD of chain transform is currently broken in Zygote, see GitHub issue #263"
+
+    @testset "AD performance" begin
+        primal, forward, pb = ad_constant_allocs_heuristic((randn(5),), (randn(10),)) do x
+            k = SEKernel() ∘ (ScaleTransform(0.1) ∘ PeriodicTransform(10.0))
+            return kernelmatrix(k, x)
+        end
+        @test primal
+        @test forward
+        @test pb
+    end
 end